具有内部近场测量的可穿透腔散射的分解方法

IF 0.9 4区数学 Q2 MATHEMATICS

Journal of Inverse and Ill-Posed Problems Pub Date : 2023-01-27 DOI:10.1515/jiip-2018-0111

Qinghua Wu, Jun Guo, G. Yan

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引用次数: 0

摘要

摘要本文研究了以层状结构为界的可穿透腔体时谐声波的逆散射问题，并试图通过内部近场测量来确定腔体的形状和位置。特别令人感兴趣的是，近场算子不满足分解方法的主要定理，因此我们引入了一个改进的近场算子，并证明了它可以用来重建空腔。数值算例验证了该算法的可行性和有效性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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The factorization method for a penetrable cavity scattering with interior near-field measurements

Abstract This paper is concerned with the inverse scattering problem of time-harmonic acoustic waves from a penetrable cavity bounded by a layered structure and seeks to determine the shape and location of the cavity from interior near-field measurements. Of particular interest is that the near-field operator does not satisfy the main theorem of the factorization method, so we introduce a modified near-field operator and prove that it can be used to reconstruct the cavity. Numerical examples demonstrate the feasibility and effectiveness of our algorithm.

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来源期刊

Journal of Inverse and Ill-Posed Problems MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.60

自引率

9.10%

发文量

审稿时长

>12 weeks

期刊介绍： This journal aims to present original articles on the theory, numerics and applications of inverse and ill-posed problems. These inverse and ill-posed problems arise in mathematical physics and mathematical analysis, geophysics, acoustics, electrodynamics, tomography, medicine, ecology, financial mathematics etc. Articles on the construction and justification of new numerical algorithms of inverse problem solutions are also published. Issues of the Journal of Inverse and Ill-Posed Problems contain high quality papers which have an innovative approach and topical interest. The following topics are covered: Inverse problems existence and uniqueness theorems stability estimates optimization and identification problems numerical methods Ill-posed problems regularization theory operator equations integral geometry Applications inverse problems in geophysics, electrodynamics and acoustics inverse problems in ecology inverse and ill-posed problems in medicine mathematical problems of tomography